Tiling the torus and other space forms
type: Item
instance of: scholarly article
title: Tiling the torus and other space forms
zbMATH Open document ID: 0627.05046
DOI: 10.1007/BF02187896
author: Marjorie Senechal
published in: Discrete \& Computational Geometry
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/131035
review text: We consider graphs on two-dimensional space forms which are quotient graphs \(\Gamma\) /F, where \(\Gamma\) is an infinite, 3-connected, face, vertex, or edge transitive planar graph and F is a subgroup of Aut(\(\Gamma)\), all of whose elements act freely on \(\Gamma\). The enumeration of quotient graphs with transitivity properties reduces to computing the normalizers in Aut(\(\Gamma)\) of the subgroups F. Results include: all isogonal toroidal polyhedra belong to the two families found by Grünbaum and Shephard; there are no transitive graphs on the Möbius band; there is a graph on the Klein bottle whose automorphism group acts transitively on its faces, edges, and vertices.
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 52Bxx
zbMATH DE Number: 4019113
zbMATH Keywords: quotient graphs
zbMATH Keywords: isogonal toroidal polyhedra
MaRDI profile type: Publication
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OpenAlex ID: W2035379096
description: scientific article; zbMATH DE number 4019113